Explanation of Tracking Risk

CFAI vol. 4, Page 18, states that “…a tracking risk of 30 bps would indicate that, in approximately two thirds of the time periods, the portfolio return will be within a band of the benchmark’s index return plus or minus 30 bps”. Isn’t this wrong? Tracking risk is the standard deviation of active returns, so by definition it is measured relative to the average active return , not the benchmark return. I suggest this alternative: a tracking risk of 30 bps would indicate that…the portfolio return will be within a band of the AVERAGE ACTIVE RETURN plus or minus 30 bps. Any comments on this?

they are right. tracking risk=portfolio return - benchmark return. so measurement is relative to the benchmark return. so benchmark return +/- 30 bps = portfolio return.

No, tracking risk is the standard deviation of active returns. Portfolio return minus benchmark return is active risk. So I still think this part of the CFAI text got it wrong.

It is interesting that this came up at this time . At work we were debating this very topic . Grinold et. al. define tracking error as standard deviation of active returns ( the one that is used in the denominator of Information Ratio) But in the industry apparently tracking error is defined more simply as root mean square of active return . The thing with the latter is that for outperformance , if you include expenses you will get SMALLER tracking error , while for underperformance root mean sq t.e. will actually increase. So a good performing portfolio will tend to get lower tracking error after fees+expenses while a poor performing portfolio will make its tracking error even worse after fees+expense. Some people even call tracking error as average of absolute annual active return, which gives a lower number that the first two

The standard deviation of active returns would only reflect the variability of an actively managed portfolio. It would not reflect how the variability differs from the benchmark. The purpose of passive management is to exhibit the same properties as the benchmark, not to eliminate risk. Tracking error is therefore the variability of returns FROM the benchmark, not overall.

agree with seemorr - active managers want higher tracking error to reflect their differing opinions (or tilts) from the benchmark i believe the CFAI text states you compare gross returns and not net returns, so you are comparing apples to apples with the benchmark if a passive manager has high tracking error that is a bad thing, since passive managers want to hug or mimic the index if an active manger has high tracking error that could be a good or bad thing (depending on whethere he/she was correct in their active mgmt decisions)

I don’t understand seemorr’s post clearly. Active returns are portfolio returns minus benchmark returns. The benchmark has no variability to itself. There is only variability in the active return. i.e. variability of the portfolio return to the benchmark return. If you mean tracking error is not standard deviation of portfolio returns , of course it isn’t.